Flexible Analysis of Individual Heterogeneity in Event Studies: Application to the Child Penalty

We provide a practical toolkit for analyzing effect heterogeneity in event studies. We develop an estimation algorithm and adapt existing econometric results to provide its theoretical justification. We apply these tools to Dutch administrative data to study individual heterogeneity in the child-penalty (CP) context in three ways. First, we document significant heterogeneity in the individual-level CP trajectories, emphasizing the importance of going beyond the average CP. Second, we use individual-level estimates to examine the impact of childcare supply expansion policies. Our approach uncovers nonlinear treatment effects, challenging the conventional policy evaluation methods constrained to less flexible specifications. Third, we use the individual-level estimates as a regressor on the right-hand side to study the intergenerational elasticity of the CP between mothers and daughters. After adjusting for the measurement error bias, we find the elasticity of 24\%. Our methodological framework contributes to empirical practice by offering a flexible approach tailored to specific research questions and contexts. We provide an open-source package ('unitdid') to facilitate widespread adoption.